Part 1 - Wholesale Customer: multivariate analysis

Dataset

You (The Wholesale Customer Dataset from UCI Machine Learning Repository¹) are a wholesale distributor in 3 regions: “Oporto” with 47 customers, “Lisbon” with 77 customers and “Other” with 316 customers, among them 298 are from the “Cafe” (including Hotels and Restaurants) distribution channel and 142 from “Retail”.

library(cluster)
library(dplyr)
library(GGally)
library(ggplot2)
library(knitr)
library(pander)
library(MASS)
library(reshape2)
library(ROCR)

sale = read.csv("WholesaleCustomer.csv", header=TRUE)
colnames(sale)[7] = "Detergents" # rename "Detergents_Paper" for brevity
sale = within(sale, {Channel[Channel == 1] <- "Cafe" 
                     Channel[Channel == 2] <- "Retail" 
                     Region[Region == 1] <- "Lisbon" 
                     Region[Region == 2] <- "Oporto" 
                     Region[Region == 3] <- "Other" } )
sale[,c("Channel", "Region")] = lapply(sale[,c("Channel", "Region")], as.factor)

Here is few rows from your annual revenue dataset:

kable(head(sale), align="c")

Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents	Delicassen
Retail	Other	12669	9656	7561	214	2674	1338
Retail	Other	7057	9810	9568	1762	3293	1776
Retail	Other	6353	8808	7684	2405	3516	7844
Cafe	Other	13265	1196	4221	6404	507	1788
Retail	Other	22615	5410	7198	3915	1777	5185
Retail	Other	9413	8259	5126	666	1795	1451

Here is how many customers with a specific revenue range for each product for each “Cafe” or “Retail” group you have

Working with log-revenues instead of revenues

The first important thing to notice is that the histograms look reasonably bell-shaped at the log-scale of revenues. Thus we transform our data from revenues to log-revenues.

Do log-numbers look unusual to you? Then you may ask: are there any other advantages of using those? Yes, log-revenues automatically care about the “percentage” difference between revenues (120 is 20% larger than 100, and 1200 is also 20% larger than 1000) rather than absolute difference. You can also think of log-value as “order of magnitude” or “count of digits in a number”. Log-revenue of 2 means revenue of 100, log-revenue of 3 means revenue of 1000, log-revenue of 4 means revenue 10000, log-revenue of 2.5 means revenue is closer to 1000 than to 100.

products = colnames(sale[,3:8]); #products
sale$Total = rowSums(sale[,products]) # total revenue
l1sale = sale;  l1sale[,3:9] = log10(1.+(sale[,3:9])) # df with logs

Analysis of variance

From the histograms above it looks like that mean revenues of Milk, Grocery and Detergent (but not necessarily of Fresh, Frozen and Delicassen) are significantly different for Cafe and Retail customers. There are parametric and non-parametric ways to test this hypothesis, with the key word being ANOVA=Analysis of variance. In such analysis the groups are considered and given and revenues as dependent variables.

Strictly speaking, ANOVA makes an assumptions on normality(which should rather be called “gaussianity”), homoscedasticity, and independence of observations. For the data set under consideration there is no doubt about independence. The other two properties are not necessarily satisfied. Practically speaking, there is a growing discussion, that many statistical methods are robust to deviations from gaussianity, and a reasonable bell-shape form of the histogram (as in our case) suffice for application of those methods. Even more, there are opinions, that normality tests should actually never be applied.

Anyway one can first resort to non-parametric Kruskal-Wallis test. Small p-values (smaller than a chosen threshold, typically 0.05) show that we can reject the hypothesis that the mean values of revenues are the same for Retail and Cafe customers. This is so for each product separately as well as for the total revenue.

apply(l1sale[,3:9], 2, function(x) kruskal.test(x ~ Channel, data=l1sale)$p.value)

##      Fresh       Milk    Grocery     Frozen Detergents Delicassen      Total 
##   1.83e-04   7.67e-38   6.60e-50   7.39e-07   4.56e-55   5.49e-04   1.72e-24

Two-sample t-test assumes gaussian distributions, but not necessarily homoscedasticity. It leads to similar results

apply(l1sale[,3:9], 2, function(x) t.test(x ~ Channel, data=l1sale, var.equal=FALSE)$p.value)

##      Fresh       Milk    Grocery     Frozen Detergents Delicassen      Total 
##   5.76e-04   3.26e-46   1.84e-68   1.39e-07   2.26e-88   5.14e-03   4.70e-28

If we consider classical anova applicable, the results are again similar

apply(l1sale[,3:9], 2, function(x) anova(lm(x ~ Channel, data=l1sale))[["Pr(>F)"]][1])

##      Fresh       Milk    Grocery     Frozen Detergents Delicassen      Total 
##   3.56e-04   1.84e-40   5.34e-57   1.94e-07   1.51e-73   5.84e-03   1.49e-22

Notice, however, that p-values for Fresh, Frozen and Delicassen are more than 25 orders of magnitude higher than for Milk, Grocery and Detergents. This reflects somehow our intuition from the histograms.

The differences between groups can be illustrated with boxplots (keep in mind though that the central line in boxplot shows median, not the mean value)

For different regions, p-values are large. Thus we cannot reject the hypothesis than mean revenues are the same

apply(l1sale[,3:9], 2, function(x) kruskal.test(x ~ Region, data=l1sale)$p.value)

##      Fresh       Milk    Grocery     Frozen Detergents Delicassen      Total 
##      0.586      0.482      0.202      0.239      0.797      0.890      0.778

Similar to the two-sample t-test, three groups can also be tested to have the same means

apply(l1sale[,3:9], 2, function(x) oneway.test(x ~ Region, data=l1sale, var.equal=FALSE)$p.value)

##      Fresh       Milk    Grocery     Frozen Detergents Delicassen      Total 
##      0.713      0.609      0.117      0.151      0.708      0.947      0.903

Results from the classical anova are also similar

apply(l1sale[,3:9], 2, function(x) anova(lm(x ~ Region, data=l1sale))[["Pr(>F)"]][1])

##      Fresh       Milk    Grocery     Frozen Detergents Delicassen      Total 
##      0.658      0.623      0.211      0.193      0.704      0.957      0.917

That difference between groups is small can be illustrated with the box- and violin-plots.

Here is the revenue comparison for different channels and different regions

Discriminant analysis

From the histograms above it looks like that the group of Retail customers differ from the group of Cafe customers in the revenues of Milk, Grocery and Detergent, while not necessarily in Fresh, Frozen and Delicassen. Is it indeed so? To formulate this question more precisely: what combinations of revenues allows one to maximally separate various groups? In such analysis the revenues are considered and given and groups as dependent variables.

LDA = Linear discriminant analysis

The most popular method is LDA. Omitting a discussion on it assumptions (multivariate gaussianity and identical covariance matrices for each group), I proceed with finding the linear combination that best separated classes

lda_ch = lda(Channel ~ ., data=l1sale[,c(1,3:8)], CV=FALSE) 
lda_ch$scaling

##                LD1
## Fresh      -0.0966
## Milk        0.4631
## Grocery     0.6784
## Frozen     -0.3453
## Detergents  1.3510
## Delicassen  0.0145

The largest contributions to it are coming from Milk, Grocery and Detergent. Keeping in mind our histograms, this does not come as a surprise. Here is the density plot versus this linear discriminant “LD1”

plot(lda_ch)

The mean values of each log-revenues for each group are

lda_ch$means

##        Fresh Milk Grocery Frozen Detergents Delicassen
## Cafe    3.87 3.34    3.45   3.27       2.58       2.85
## Retail  3.64 3.92    4.13   2.97       3.73       3.00

The quality of separation can be estimated by the ratio of the between- and within-group standard deviations

lda_ch$svd

## [1] 23.7

To estimate the quality of classification produced by the LDA we should use not the training set, but resort to cross validation. Since leave-one-out cross validation is built-in, let us use it. Here are the confusion matrix and the total percent of correctly classified customers

lda_ch_cv = lda(Channel ~ ., data=l1sale[,c(1,3:8)], CV=TRUE) 
ct_lda <- table(l1sale$Channel, lda_ch_cv$class); ct_lda # confusion matrix

##         
##          Cafe Retail
##   Cafe    273     25
##   Retail   13    129

#diag(prop.table(ct, 1))  # percent correct for each Channel
sum(diag(prop.table(ct_lda))) # total percent correct

## [1] 0.914

This method can also provides the posterior probabilities of belonging to each group. Thus, we can asses the quality of the model with respect to more refined measures. Below, after discussing QDA, I will plot the ROC curve and calculate AUC.

QDA = Quadratic discriminant analysis

QDA differs from LDA in that it does not assume a common covariance matrix for all classes. This leads to more free parameters and thus to larger flexibility of the method. Since QDA uses quadratic functions, there are no easily interpretable linear discriminants. We can use this method to make predictions for unknown samples (here via leave-one-out cross validation). This results in the following confusion matrix and the total percent of correctly classified customers. The results appears to be a little worse than those for LDA

qda_ch_cv = qda(Channel ~ ., data=l1sale[,c(1,3:8)], CV=TRUE, method="mle")
ct_qda <- table(l1sale$Channel, qda_ch_cv$class); ct_qda # confusion matrix

##         
##          Cafe Retail
##   Cafe    269     29
##   Retail   13    129

#diag(prop.table(ct, 1))  # percent correct for each Channel
sum(diag(prop.table(ct_qda))) # total percent correct

## [1] 0.905

Comparing ROC curves

roc_auc = function(da){
    pred = prediction(predictions=da$posterior[,"Retail"], 
                      labels=as.numeric(l1sale$Channel=="Retail"))
    perf <- performance(pred, measure = "tpr", x.measure = "fpr")
    roc.auc = performance(pred, measure="auc"); 
    return(list(perf=perf, auc=roc.auc@y.values[[1]]))
}

lda_roc_auc = roc_auc(lda_ch_cv)
qda_roc_auc = roc_auc(qda_ch_cv)

cutoffs = c(0.2,0.4, 0.5, 0.6, 0.8)
plot(lda_roc_auc$perf, colorize=TRUE, lwd=3, 
     main="ROC curve for LDA and QDA prediction of Retail channel",
     print.cutoffs.at=cutoffs, text.adj=c(1.0,-0.5))
plot(qda_roc_auc$perf, colorize=TRUE, lwd=3, main="ROC curve for LDA prediction of Retail channel", 
     add=TRUE)
text(-0.03, 0.99, "LDA", pos=4)
text(0.1, 0.85, "QDA", pos=4)
text(0.15,0.6,paste0("LDA  AUC = ", round(lda_roc_auc$auc,3)), pos=4)
text(0.2,0.5,paste("cutoff positions at", paste(cutoffs, collapse=", ")),  pos=4)
text(0.15,0.3,paste0("QDA  AUC = ", round(qda_roc_auc$auc,3)), pos=4)

The results of discriminant analysis should typically be compared with other classification methods such as logistic regression, support vector machines, neural nets.

Factor analysis

Revenues for some products are correlated with each other

l1sale.cor = cor(l1sale[,products]); l1sale.cor

##              Fresh    Milk Grocery  Frozen Detergents Delicassen
## Fresh       1.0000 -0.0211  -0.133  0.3863     -0.159      0.256
## Milk       -0.0211  1.0000   0.761 -0.0552      0.679      0.342
## Grocery    -0.1330  0.7611   1.000 -0.1645      0.797      0.240
## Frozen      0.3863 -0.0552  -0.165  1.0000     -0.213      0.256
## Detergents -0.1587  0.6787   0.797 -0.2128      1.000      0.168
## Delicassen  0.2564  0.3423   0.240  0.2563      0.168      1.000

Let us try to determine the (independent) latent variables responsible for the variety of the observed revenues. Suitable here is exploratory factor analysis.

faa2 = factanal(l1sale[,products], factors=2, method="mle", rotation="varimax", scores="regression")
print(faa2, digits = 2, cutoff = .2, sort = TRUE)

## 
## Call:
## factanal(x = l1sale[, products], factors = 2, scores = "regression",     rotation = "varimax", method = "mle")
## 
## Uniquenesses:
##      Fresh       Milk    Grocery     Frozen Detergents Delicassen 
##       0.65       0.30       0.13       0.61       0.26       0.65 
## 
## Loadings:
##            Factor1 Factor2
## Milk        0.83          
## Grocery     0.93          
## Detergents  0.84          
## Fresh               0.58  
## Frozen              0.61  
## Delicassen  0.31    0.51  
## 
##                Factor1 Factor2
## SS loadings       2.38    1.01
## Proportion Var    0.40    0.17
## Cumulative Var    0.40    0.57
## 
## Test of the hypothesis that 2 factors are sufficient.
## The chi square statistic is 4.41 on 4 degrees of freedom.
## The p-value is 0.353

The chi-square statistic and p-value in “factanal” are the results of testing the hypothesis that the model fits the correlation matrix perfectly. When the p value is large (larger than your confidence level, typically 0.05), as it is here, we cannot reject this hypothesis. Thus, 2 factors are enough to explain the empirical covariance matrix.

Let us check how well the true correlation matrix is approximated by the fitted one by computing difference between them. As expected, all differences are very small.

faa2.cor.approx <- faa2$loadings %*% t(faa2$loadings) + diag(faa2$uniquenesses)
round(l1sale.cor - faa2.cor.approx, 3)

##             Fresh   Milk Grocery Frozen Detergents Delicassen
## Fresh       0.000 -0.011  -0.001  0.021      0.014     -0.010
## Milk       -0.011  0.000  -0.001 -0.014     -0.003      0.027
## Grocery    -0.001 -0.001   0.000  0.008      0.002     -0.007
## Frozen      0.021 -0.014   0.008  0.000     -0.001     -0.012
## Detergents  0.014 -0.003   0.002 -0.001      0.000     -0.010
## Delicassen -0.010  0.027  -0.007 -0.012     -0.010      0.000

Since factors are determined up to rotations, we have chosen the “varimax” rotation. This sparsifies the contribution of individual products and thus makes interpretation easier.

2 factors can explain 57% of data variance.

Factor1: mainly the sum of revenues for Milk, Grocery and Detergents
Factor2: mainly the sum of Fresh, Frozen and Delicassen

The exact contribution of each product to factor is shown here

ggplot(as.data.frame(unclass(faa2$loadings)), 
                           aes(x=Factor1, y=Factor2) ) + geom_text(label=products) + 
            theme_bw(base_size = 16) + ggtitle("Contribution of products to the two latent factors")

And here are the two factors (found by “factanal”) for each customer

Large uniquenesses show, however, that there is much more in this data than can be explained by two factors.

faa2$uniqueness

##      Fresh       Milk    Grocery     Frozen Detergents Delicassen 
##      0.654      0.296      0.133      0.613      0.263      0.646

For each of the Fresh, Frozen and Delicassen more than 60% of the variability of revenue is not explained by the common factors.

Cluster analysis

Cluster analysis answer the questions: which customers belong together and can be combined in a group such that this group is noticeably different from other groups (formed on the same principle). Here I choose to work only with revenue data, in order to be able to check how the found clusters are related to known distribution channels and regions.

Cluster analysis is very sensitive to the meaningful distance between customers. And defining what “meaningful distance between customers” is, is crucial for inferring business value.

A business user should ask himself

do I care more about the absolute revenues (rather log-revenues in our analysis) or do I accept that for some products (Fresh, for example) revenues are generally higher than for others (Delicassen, for example) and I care more about the difference between the actual and the mean revenues for a given product

A mathematically aware business user should also ask himself

with 440 customers and 6 products I am operating with 440 points in 6D space. Does this makes sense or am I (my data, actually) under the curse of dimensionality? Should I perform dimensionality reduction?
how different is different? or, in mathematical terms, is my distance euclidean, manhattan or something else?

Agglomerative hierarchical clustering suggest 2 or 3 clusters

As good business user as I am, I am choosing to care about the difference to the mean, reduce dimensionality to 4, and use manhattan distance.

scaled.pca4 = princomp(scale(l1sale[,products]))$scores[,1:4]
di = dist(scaled.pca4, method="manhattan")  # manhattan distance

For agglomerative hierarchical clustering I choose “Ward” clustering method. It minimizes the total within-cluster variance and thus leads to most compact clusters possible.

ag = agnes(di, diss=TRUE, method="ward")
plot(ag, which=2, labels=FALSE, xlab="", sub="", 
     main="Dendogram: 4-comp PCA, manhattan distance, Ward agglomeration") # dendrogram

The dendrogram suggest that 2 or 3 clusters are meaningful. Let us investigate 3 clusters

l1sale$ag3 <- factor(cutree(ag, k = 3))
table(l1sale$Channel, l1sale$ag3, dnn=c("Channel", "ag3") )

##         ag3
## Channel    1   2   3
##   Cafe    22  50 226
##   Retail  56  81   5

The third cluster consists mainly of Cafe customers, while the first and the second one include both Cafe and Retail. What about the revenues for each product?

This set of boxplots shows that Group 3 (nearly all of those Cafe customers) buy less Milk, Grocery and Detergents than the other two groups. Among groups with mixed Cafe and Retail customers, groups 1 (30% Cafe 70% Retail low-revenue customers) buys less Fresh, Frozen and Delicassen that group 2 (40% Cafe 60% Retail high-revenue customers). That’s how these groups look like, when I choose axis as sum of revenues

Thus, the 3 groups found are

40/60 mix Cafe Retail with low-to-middle total revenues due to low Fresh, Frozen
30/70 mix Cafe/Retail with high total revenues
Cafe customers with low total revenues due to low Milk, Grocery and Detergents

Let us depict customers versus easily interpretable axes: sums of revenues of specific products. The 3 “groups” found do not look like compact at all.

Can it be related to the “unfortunate” choice of axes? Let us try with the “most fortunate” possible axis (the first two PCA components)

clusplot(l1sale[,products], l1sale$ag3, color=TRUE, shade=FALSE, labels=3, lines=0,
         col.p=group_color[as.integer(l1sale$ag3)], 
         col.clus=group_color[c(1,3,2)],
         main="3 groups found by hierarchical clustering")

No success either. How shall we interpret this?

A good tool to assess the quality of clustering is the silhouette diagram. It shows which objects lie well within their cluster, and which ones are merely somewhere in between clusters.

si.ag3 = silhouette(as.numeric(l1sale$ag3), di); 
plot.silhouette(si.ag3, col=group_color, 
                main="Silhouette plot for 3 groups from aglomerative clustering")

With more than few negative values the silhouette diagram does not look good. With average silhouette widths of 0.10, 0.29 and 0.25, the clustering should be assessed as “no substantial structure has been found”.

Partitioning around medoinds: a robust version of K-means

Let us look at the 3 cluster from the point of view of K-medoids algorithms. This can be considered as a more robust version of k-means, which searches for k representative objects (“medoids”) among data points. These “medoid customers” should represent the “typical customer” of the group.

pam3 = pam(di, k=3, diss=TRUE, cluster.only=FALSE)
l1sale$pam3 = as.factor(pam3$cluster)
table(l1sale$Channel, l1sale$pam3, dnn=c("Channel", "pam3")) # compare clusters distribution Channels

##         pam3
## Channel    1   2   3
##   Cafe    20 162 116
##   Retail 115   2  25

Groups 2 and 3 consist mainly of Cafe customers, while group 1 from Retail customers. The separation of distribution channels here is better than one achieved in the agglomerative hierarchical clustering. What is the difference in revenues?

Thus, the 3 groups found are

mostly Retail customers with high Milk, Grocery, Detergent revenues
mostly Cafe customers with low Milk, Grocery, Detergent revenues
mostly Cafe customers with medium Milk, Grocery, Detergent revenues

The difference between Fresh, Frozen and Delicassen for all groups is relatively small

Here are the log-revenues of the “typical customers” found

l1sale[pam3$medoids, c("pam3", products, "Total")]

##     pam3 Fresh Milk Grocery Frozen Detergents Delicassen Total
## 417    1  3.64 4.04    4.04   2.93       3.83       3.00  4.54
## 116    2  4.05 2.90    3.48   3.43       2.44       2.79  4.27
## 315    3  4.03 3.25    3.88   3.17       2.93       3.09  4.37

With sums of revenues of specific products on axis, here are the 3 customer “groups”

This is a pretty much different clustering than the one found by the agglomerative method.

Does partitioning around medoids indeed found distinct clusters in this dataset? Silhouette plot (low values of silhouette width) again indicates no significant structure in data.

si.pam3 = silhouette(as.numeric(l1sale$pam3), di)
plot.silhouette(si.pam3, col=group_color, main="Silhouette plot for 3 groups found by PAM")

What to do or is clustering meaningful for this dataset?

Having done the cluster analysis, several questions are pending

Do these results actually mean that our customers cannot be structured?
Is it meaningful for this data to assume that there are several distinct groups and enforce searching for distinct groups?

If one still wants to search for distinct groups, it may be reasonable to reconsider what the “distance between customers” mean. As it was shown with histograms and boxplots, the main difference lies in 3 products out of 6. At the same time, the distance considered so far tried to take into account all 6. The ways out of this situation (and out of the curse of dimensionality) I will discuss in the more extensive “Wholesale Customers: cluster analysis” write-up. Ideally it would be nice not to guess the appropriate distance matrix, but let the algorithm to determine it.

Here I discuss another question: why are we actually trying so hard to “put a single label” on each customer?

I am aiming at more natural “segmentation” of customers, which behave somehow “in the same way” with respect to at least some products (even though there are no distinct groups). Neighbor segments should be similar. Thus it will be not so important to which segment exactly a given customer belongs and how many segments exactly there are.

Customer segmentation

Similar customers are in one segment. Neighbor segments are similar to each other in some products.

The upper circles in this visualization are for Milk, Grocery, Detergents. Large revenues of those, as we know from the previous analysis are typical for Retail customers.

Some segments are pretty interesting. Here we display actual revenues instead of log-revenues

Customers in segment 5 are buying very little (in comparison to average values) Fresh, Frozen and Delicassen. Shouldn’t you (as a careful businessmen) check why and what is going on?

ID	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents	Delicassen	Total
67	Cafe	Other	9	1534	7417	175	3468	27	12630
129	Cafe	Other	140	8847	3823	142	1062	3	14017
185	Cafe	Other	327	918	4710	74	334	11	6374
204	Cafe	Lisbon	583	685	2216	469	954	18	4925
234	Cafe	Lisbon	964	4984	3316	937	409	7	10617
413	Cafe	Other	97	3605	12400	98	2970	62	19232
440	Cafe	Other	2787	1698	2510	65	477	52	7589

Customers in segment 6 are buying very little Milk, Grocery, Detergent. Are you sure that you are a careful businessmen?

ID	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents	Delicassen	Total
76	Cafe	Other	20398	1137	3	4407	3	975	26923
123	Cafe	Other	12212	201	245	1991	25	860	15534
162	Cafe	Other	12434	540	283	1092	3	2233	16585
357	Cafe	Other	22686	134	218	3157	9	548	26752

Customers in segment 15 need everything except Frozen. Why? Can it be that donating a refrigerator to them will boost their Frozen revenue to the level of other products (which are not small, by the way)? Is there a practice of such donations in the industry?

ID	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents	Delicassen	Total
17	Retail	Other	1020	8816	12121	134	4508	1080	27679
39	Retail	Other	4591	15729	16709	33	6956	433	44451
58	Retail	Other	5417	9933	10487	38	7572	1282	34729
60	Cafe	Other	6137	5360	8040	129	3084	1603	24353
61	Retail	Other	8590	3045	7854	96	4095	225	23905
95	Retail	Other	5626	12220	11323	206	5038	244	34657
107	Retail	Other	1454	6337	10704	133	6830	1831	27289
146	Retail	Other	22039	8384	34792	42	12591	4430	82278
156	Retail	Other	1989	10690	19460	233	11577	2153	46102
176	Retail	Other	2343	7845	11874	52	4196	1697	28007
217	Retail	Lisbon	2532	16599	36486	179	13308	674	69778
222	Cafe	Lisbon	5396	7503	10646	91	4167	239	28042
246	Retail	Lisbon	3062	6154	13916	230	8933	2784	35079
265	Retail	Lisbon	1073	9679	15445	61	5980	1265	33503
334	Retail	Oporto	8565	4980	67298	131	38102	1215	120291
419	Retail	Other	660	8494	18622	133	6740	776	35425
421	Cafe	Other	4456	5266	13227	25	6818	1393	31185

Customers in segment 23 look like really large Cafes. Why do they want so little Detergents? Do they stick to some specific brand that you do not have?

ID	Channel	Region	Fresh	Milk	Grocery	Frozen	Detergents	Delicassen	Total
24	Retail	Other	26373	36423	22019	5154	4337	16523	110829
88	Cafe	Other	43265	5025	8117	6312	1579	14351	78649
182	Cafe	Other	112151	29627	18148	16745	4948	8550	190169
184	Cafe	Other	36847	43950	20170	36534	239	47943	185683
203	Cafe	Lisbon	25203	11487	9490	5065	284	6854	58383
266	Cafe	Lisbon	5909	23527	13699	10155	830	3636	57756
326	Cafe	Oporto	32717	16784	13626	60869	1272	5609	130877
385	Cafe	Other	10683	21858	15400	3635	282	5120	56978
436	Cafe	Other	29703	12051	16027	13135	182	2204	73302

Do you want to know more? Actually how similar are customers in a given segment? How similar is a segment to its neighbors? I can tell you about this personally. I also found 3 more segments that arise questions and opportunities.

Contact: Olga Lalakulich olalakul@gmail.com

References

https://archive.ics.uci.edu/ml/datasets/Wholesale+customers The data set is originated from a larger database referred on: Abreu, N. (2011). Analise do perfil do cliente Recheio e desenvolvimento de um sistema promocional. Mestrado em Marketing, ISCTE-IUL, Lisbon↩

Wholesale Customers: multivariate analysis

Olga Lalakulich